class_docstr: Class for the manifold of positive reals.
  
  The real positive axis endowed with the Information geometry metric.
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docstr: Check if a point is a positive real.
  
  Evaluate if a point belongs to the positive real axis,
  i.e. evaluate if its norm is lower than one.
  
  Parameters
  ----------
  point : array-like, shape=[..., 1]
      Points to be checked.
  atol : float
      Tolerance.
      Optional, default: backend atol.
  
  Returns
  -------
  belongs : array-like, shape=[...]
      Boolean denoting if point is a positive real.
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code: def belongs(point, atol=gs.atol):
      """Check if a point is a positive real.
  
      Evaluate if a point belongs to the positive real axis,
      i.e. evaluate if its norm is lower than one.
  
      Parameters
      ----------
      point : array-like, shape=[..., 1]
          Points to be checked.
      atol : float
          Tolerance.
          Optional, default: backend atol.
  
      Returns
      -------
      belongs : array-like, shape=[...]
          Boolean denoting if point is a positive real.
      """
      if point.shape[-1] != 1:
          return gs.zeros(point.shape[:-1], dtype=bool)
  
      is_real = gs.all(gs.abs(gs.imag(point)) < atol, axis=(-1,))
      is_positive = gs.all(gs.real(point) > 0, axis=(-1,))
  
      res = gs.logical_and(is_positive, is_real)
      if not gs.is_array(res):
          return gs.array(res)
  
      return res
  
file_path: geomstats/geomstats/geometry/positive_reals.py
imports: import geomstats.backend
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
label_desc: Use image node_id 3 for calling the PositiveReals obj's underlying member method code with example usage: obj.belongs(point, atol) and returns: res, gs, gs